Popular periodicals are the kind you would buy to read for fun - magazines and newspapers. They may have some value for research, depending on the topic, but they are usually not the best type of resource for college-level research.
Scholarly periodicals (journals and peer-reviewed journals) are written for and by people who work in academics: professors, researchers, undergraduate or graduate students. This type of article is best suited for your research because it is reliable and authoritative. Many of these are peer-reviewed.
Conference Proceedings are a great place to find cutting edge research - if the conference is scholarship-based (rather than trade-based), you can expect to find cutting-edge scholarly ideas. Search in scholarly periodicals for further articles about an idea or theory you find in conference proceedings.
Trade publications are written by specialists in an industry. While sources are mentioned, they are rarely formally cited. There is generally no peer-review process, and articles tend to include practical information aimed at people in a particular professional, trade or industry. Trade publications are not considered scholarly sources.